Multiple constant multiplications: efficient and versatile framework and algorithms for exploring common subexpression elimination

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 15, Issue 2, 1996, Pages 151-165

  Potkonjak, Miodrag ^a   Srivastava, Mani B ^a   Chandrakasan, Anantha P ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPLICATION SPECIFIC INTEGRATED CIRCUITS; COMPUTATIONAL METHODS; DIGITAL ARITHMETIC; HEURISTIC METHODS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; PROBLEM SOLVING;

ITERATIVE PAIRWISE MATCHING HEURISTIC; MULTIPLE CONSTANT MULTIPLICATIONS; SCALING TRANSFORMATION; SUBEXPRESSION ELIMINATION;

COMPUTER AIDED LOGIC DESIGN;

EID: 0030086034     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/43.486662     Document Type: Article

References (66)

1. D. E. Knuth The Art of Computer Programming: Volume 2: Seminumerical Algorithms 2nd 1981 Addison-Wesley MA, Reading
2. D. Ku G. De Micheli Constrained Synthesis and Optimization of Digital Circuits from Behavioral Specifications 1992 Kluwer Academic MA, Boston
3. U. W. Kulish W. L. Miranker The arithmetic of the digital computer: A new approach SIAM Rev. 28 1 1𔃘
4. D. A. Lobo B. M. Pangrle Redundant operator creation: A scheduling optimization technique 28th Design Automation Conf. 775 778 1991
5. O. L. MacSorley High-speed arithmetic in binary computers Proc. IRE 49 1 67 91 1961
6. D. J. Magenheimer L. Peters K. Pettis D. Zuras Integer multiplication and division on the HP precision architecture 2nd Int. Conf. Architectural Support Programming Languages Operating Systems (ASPLOS II) 90 99 1987 IEEE Computer Soc. Press DC, Washington
7. D. J. Magenheimer L. Peters K. Pettis D. Zuras Integer multiplication and division on the HP precision architecture IEEE Trans. Comput. 37 980 990 1988 12 137 2248
8. P. Mazumder J.-S. Yih Neural computing for build-in-self-repair of embedded memory arrays Int. Symp. Fault‐Tolerant Computing 480 487 1989 IL, Chicago 251 3238 105623
9. W. M. McKeeman Peephole optimization Commun. ACM 8 7 443 444 1965
10. D. E. Muller Application of Boolean algebra to switching circuits design and error detection IRE Trans. Electron. Comput. 3 6 6 12 1954
11. I. Nakata On compiling algorithms for arithmetic expressions Commun. ACM 10 492 494 1967
12. K. K. Parhi Algorithm transformation technique for concurrent processors Proc. IEEE 77 1879 1895 1989 5 1815 48830
13. J. O. Penhollow Study of arithmetic recording with applications in multiplication and division Sept. 1962 Ph.D. dissertation Urbana
14. M. B. Srivastava M. Potkonjak Transforming linear systems for joint latency and throughput optimization EDAC-94 267 271 1994 946 7755 326866 paper 5B-2
15. A. S. Tanenbaum H. van Straven J. W. Stevenson Using peephole optimization on intermediate code ACM Trans. Programm. Languages Syst. 4 1 21 36 1982
16. W. M. Waite G. Goos Compiler Construction 1984 Springer-Verlag New York
17. R. A. Walker D. E. Thomas Behavioral transformation for algorithmic level IC design IEEE Trans. Computer‐Aided Design 8 1115 1127 Oct. 1989 43 1541 39073
18. R. A. Walker R. Camposano A Survey of High‐Level Synthesis Systems 1991 Kluwer Academic MA, Boston
19. S. Wolfram Mathematica: A System for Doing Mathematics by Computer 1991 Addison-Wesley CA, Redwood City
20. W. Wulf R. K. Johnson C. B. Weinstock S. O. Hobbs C. M. Geschke The Design of Optimizing Compiler 1975 North Holland New York
21. N. Ahmed K. R. Rao Orthogonal Transform for Digital Signal Processing. 1975 Springer-Verlag New York
22. A. V. Aho S. C. Johnson J. D. Ullman Code generation for expressions with common subexpressions J. ACM 24 1 146 160 1977
23. P. Beame R. Impagliazzo J. Krajicek T. Pitassi P. Pudlak A. Woods Exponential lower bounds for the pigeonhole principle 24th Ann. ACM Symp. Theory of Computing 200 221 1992
24. R. Bernstein Multiplication by integer constants Software̵Practice and Experience 16 7 641 652 1986
25. R. E. Blahut Theory and Practice of Error Control Codes. 1983 Addison-Wesley MA, Reading
26. R. E. Blahut Fast Algorithms for Digital Signal Processing. 1985 Addison-Wesley MA, Reading
27. A. D. Booth A signed binary multiplication technique Quat. J. Mach. App. Math. IV 2 236 240 1951
28. R. C. Bose D. K. Ray-Chaudhuri On a class of error-correcting binary group codes Inform. Contr. 3 1 68 79 1960
29. R. K. Brayton G. D. Hachtel C. T. McMullen A. L. Sangiovanni-Vincentelli Logic Minimization Algorithms for VLSI Synthesis 1984 Kluwer Academic MA, Boston
30. G. De Micheli A. Sangiovanni-Vincentelli P. Antogneti Algorithms for multi-level logic synthesis and optimization Design Systems for VLSI Circuits: Logic Synthesis and Silicon Compilation 197 248 1987 Martinus Nijhoff The Netherlands, Dordrecht
31. R. K. Brayton R. Rudell A. Sangiovanni-Vincentelli A. R. Wang MIS: A multiple-level logic optimization system IEEE Trans. Computer‐Aided Design CAD-6 1062 1081 1987
32. R. W. Brodersen Anatomy of a Silicon Compiler. 1992 Kluwer Academic MA, Boston
33. J. Bruno R. Sethi Code generation for a one-register machine ACM 23 4 502 510 1976
34. A. W. Burks H. Goldstine J. von Neumann Preliminary discussion of the logical design of an electronic computing instrument June 1947 Institute for Advanced Studies NJ, Princeton Tech. Rep.
35. V. A. Busam D. E. Englund Optimization of expressions in FORTRAN Commun. ACM 12 2 666 674 1969
36. F. Catthoor SAMURAI: A general and efficient simulated annealing schedule with fully adaptive annealing parameters Integration 6 147 178 1988
37. A. Chandrakasan M. Potkonjak J. Rabaey R. W. Brodersen HYPER-LP: A system for power minimization using architectural transformations Proc. IEEE ICCAD‐92 300 303 1992 894 6927 279357
38. A. Chatterjee R. K. Roy An architectural transformation program for optimization of digital systems by multi-level decomposition 30th ACM/IEEE Design Automation Conf. 343 348 1993
39. A. Chatterjee R. K. Roy M. A. d'Abreu Greedy hardware optimization for linear digital systems using number splitting and repeated factorization IEEE Trans. VLSI Syst. 1 423 431 1993 92 6405 250189
40. J. Cocke J. T. Schwartz Programming Languages and Their Compilers: Preliminary Notes 1970 Courant Inst. Math. Sci. New York
41. T. H. Cormen C. E. Leiserson R. L. Rivest Introduction to Algorithms 1990 MIT Press MA, Cambridge
42. A. P. Ershov On programing of arithmetic operations Commun. ACM 1 8 3 6 1958
43. E. Feig S. Winograd Fast algorithms for the discrete cosine transform IEEE Trans. Signal Processing 40 2174 2193 1992 78 4075 157218
44. C. N. Fischer R. J. LeBlanc Jr. Crafting a Compiler 1991 Benjamin/Cummings CA, Menlo Park
45. J. C. Gibson The Gibson mix 1970 IBM Systems Develop. Div. NY, Poughkeepsie Rep. TR 00.2043
46. G. H. Golub C. van Loan Matrix Computation 1989 The Johns Hopkins Univ. Press MD, Baltimore
47. D. Goldberg What every computer scientist should know about floating-point arithmetic ACM Comput. Surveys 23 1 5 48 1991
48. Graham D. E. Knuth O. Patashnik Concrete Mathematics: A Foundation for Computer Science 1989 Addison-Wesley MA, Reading
49. L. Guerra M. Potkonjak J. Rabaey High level synthesis for reconfigurable datapath structures IEEE Proc. ICCAD 26 29 1993 4431 12568 580026
50. L. Guerra M. Potkonjak J. Rabaey Concurrency characteristics in DSP programs 1994 Int. Conf. Acoustic, Speech, Signal Processing 2 433 436 1994 3104 8835 389628
51. K. Hwang Computer Arithmetic: Principle, Architecture, and Design 1979 Wiley New York
52. Z. Iqbal M. Potkonjak S. Dey A. Parker Critical path minimization using retiming and algebraic speed-up ACM/IEEE Design Automation Conf. 573 577 1993
53. R. Karri A. Orailoglu Transformation-based high-level synthesis of fault-tolerant ASIC's Design Automation Conf. 662 665 1992 411 5909 227803
54. M. Potkonjak J. Rabaey Optimizing resource utilization using transformations IEEE ICCAD91 88 91 1991 CA, Santa Clara 345 4745 185199
55. M. Potkonjak J. Rabaey Maximally fast and arbitrarily fast implementation of linear computations ICCAD‐92 304 308 1992 894 6927 279356
56. J. Rabaey C. Chu P. Hoang M. Potkonjak Fast prototyping of data path intensive architecture IEEE Design Test 8 40 51 1991 54 2692 82037
57. K. R. Rao P. Yip Discrete Cosine Transform: Algorithms, Advantages, Applications 1990 Academic MA, Boston
58. R. R. Redziejowski On arithmetic expressions and tress Commun. ACM 12 2 81 84 1969
59. I. S. Reed A class of multiple-error-correcting codes and the decoding scheme IRE Trans. Electron. Comput. 4 1 38 49 1954
60. M. Y. Rhee Error‐Correcting Coding Theory 1989 McGraw-Hill New York
61. G. W. Reitwiesner Binary arithmetic Advances in Computers 1 261 265 1960 Academic New York
62. J. E. Robertson Theory of computer arithmetic employed in the design of the computer at the University of Illinois June 1960 Digital Computer Lab., Univ. Illinois Urbana
63. K. Roy S. C. Prasad Circuits activity based logic synthesis for low power reliable operations IEEE Trans. VLSI Syst. 1 503 513 1993 92 6405 250198
64. H. Samueli An improved search algorithm for optimization of the FIR coefficients represented by a canonic signed-digit code IEEE Trans. Circuits Syst. 34 1192 1202 1987
65. M. Schictel $G2$ blend surfaces and filling of $N$-sided holes IEEE Comp. Graphics Appl. 13 68 73 1993 38 6002 232100
66. R. Sethi J. D. Ullman The generation of optimal code for arithmetic expressions ACM 17 4 715 728 1970